The function of power distribution systems is delivering the electric powers from the transmission systems to the customers. The distribution system may be either a 3-phase 4 wire system, or a 3-phase 3 wire system. The power from transmission system or distribution generators are delivered to the customers through transmission lines, and various voltage regulating devices, such as voltage regulators, two-winding or three-winding transformers. The customer loads may be of single phase, or three-phase. The loads may be constant power load, constant current load or constant impedance load.
FIG. 1 shows schematic diagrams of a sample distribution system including both the three-phase representation 101 and one-line diagram 102. The sample system includes one Delta-connected three-phase source 110, two three-phase transmission lines 120 and 140, one Delta-connected three-phase load 150, and one two-winding transformer 130 with Wye/Delta connection. There are four three-phase buses in the system, including bus 115, bus 125, bus 135 and bus 145. This sample distribution system is an ungrounded distribution system.
The purpose of three-phase power flow analysis is to obtain the voltages at each phase of any bus in the distribution system, for specified source and load conditions. After the voltages are known, currents and powers in each branch on each phase, as well as the output of the generation sources, can be determined analytically.
The ungrounded distribution system is a special case of distribution system. It adopts three phase three wire configuration. The windings of transformers or voltage regulators use Delta, ungrounded Wye, or open Delta connection. Delta or open Delta connections are commonly used for the distribution loads or shunt capacitors. The effectiveness of power flow methods are heavily depended on what type of devices is modeled, and how the device is connected in itself and with other ones.
Depending on known parameters, buses of the distribution system can be classified as (1) a swing bus, if the voltage magnitude |V| and the phase angle θ are known; (2) as a PQ bus, if the active power P and the reactive power Q are known; and (3) as a PV bus, the active power P and voltage magnitude |V| are known. The bus type is determined by the known parameters of connected sources and loads.
Various methods for solving three phase power flow problem are known. Those methods differ in either the form of the equation describing the system, or the numerical techniques used, and usually are either topology based or matrix based. Typical topology based methods include backward/forward sweep method, and ladder method. Typical matrix based methods include implicit Z-bus matrix method, Newton-Raphson method, and Fast Decoupled method. All of those methods have their own limitations when applied to large systems either in modeling capabilities or computational efficiency.